Randomized mesh design

ABSTRACT

In one embodiment, an apparatus may include a touch sensor that includes a mesh of conductive material. The mesh includes a number of mesh cells that each have a number of vertices. Each of the vertices has a substantially randomized location within an annulus centered at a seed location of the vertex. The apparatus may also include one or more computer-readable non-transitory storage media coupled to the touch sensor and embodying logic that is configured when executed to control the touch sensor.

TECHNICAL FIELD

This disclosure generally relates to touch sensors.

BACKGROUND

An array of conductive drive and sense electrodes may form a mutual-capacitance touch sensor having one or more capacitive nodes. The mutual-capacitance touch sensor may have either a two-layer configuration or single-layer configuration. In a single-layer configuration, drive and sense electrodes may be disposed in a pattern on one side of a substrate. In such a configuration, a pair of drive and sense electrodes capacitively coupled to each other across a space or dielectric between electrodes may form a capacitive node.

In a single-layer configuration for a self-capacitance implementation, an array of vertical and horizontal conductive electrodes may be disposed in a pattern on one side of the substrate. Each of the conductive electrodes in the array may form a capacitive node, and, when an object touches or comes within proximity of the electrode, a change in self-capacitance may occur at that capacitive node and a controller may measure the change in capacitance as a change in voltage or a change in the amount of charge needed to raise the voltage to some pre-determined amount.

In a touch-sensitive display application, a touch screen may enable a user to interact directly with what is displayed on a display underneath the touch screen, rather than indirectly with a mouse or touchpad. A touch screen may be attached to or provided as part of, for example, a desktop computer, laptop computer, tablet computer, personal digital assistant (PDA), smartphone, satellite navigation device, portable media player, portable game console, kiosk computer, point-of-sale device, or other suitable device. A control panel on a household or other appliance may include a touch screen.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example touch sensor with an example controller.

FIG. 2 illustrates example mesh cells with example vertices having substantially randomized locations.

FIG. 3 illustrates example dual-layer mesh cells with example vertices having substantially randomized locations.

FIG. 4 illustrates an example placement of example seed locations relative to an example display.

FIG. 5 illustrates an example method for designing a conductive mesh with randomized vertices.

FIG. 6 illustrates an example computer system.

DESCRIPTION OF EXAMPLE EMBODIMENTS

FIG. 1 illustrates an example touch sensor 10 with an example touch-sensor controller 12. Touch sensor 10 and touch-sensor controller 12 may detect the presence and location of a touch or the proximity of an object within a touch-sensitive area of touch sensor 10. Herein, reference to a touch sensor may encompass both the touch sensor and its touch-sensor controller, where appropriate. Similarly, reference to a touch-sensor controller may encompass both the touch-sensor controller and its touch sensor, where appropriate. Touch sensor 10 may include one or more touch-sensitive areas, where appropriate. Touch sensor 10 may include an array of drive and sense electrodes (or an array of electrodes of a single type) disposed on one or more substrates, which may be made of a dielectric material. Herein, reference to a touch sensor may encompass both the electrodes of the touch sensor and the substrate(s) that they are disposed on, where appropriate. Alternatively, where appropriate, reference to a touch sensor may encompass the electrodes of the touch sensor, but not the substrate(s) that they are disposed on.

An electrode (whether a ground electrode, a guard electrode, a drive electrode, or a sense electrode) may be an area of conductive material forming a shape, such as for example a disc, square, rectangle, thin line, other suitable shape, or suitable combination of these. One or more cuts in one or more layers of conductive material may (at least in part) create the shape of an electrode, and the area of the shape may (at least in part) be bounded by those cuts. In particular embodiments, the conductive material of an electrode may occupy approximately 100% of the area of its shape. As an example and not by way of limitation, an electrode may be made of an optically clear conductive material, such as for example indium tin oxide (ITO) and the ITO of the electrode may occupy approximately 100% of the area of its shape (sometimes referred to as 100% fill), where appropriate. In particular embodiments, the conductive material of an electrode may occupy substantially less than 100% of the area of its shape. As an example and not by way of limitation, an electrode may be made of fine lines of metal or other conductive material (FLM), such as for example copper, silver, or a copper- or silver-based material, and the fine lines of conductive material may occupy approximately 5% of the area of its shape in a hatched, mesh, or other suitable pattern. Herein, reference to FLM encompasses such material, where appropriate. Although this disclosure describes or illustrates particular electrodes made of particular conductive material forming particular shapes with particular fill percentages having particular patterns, this disclosure contemplates any suitable electrodes made of any suitable conductive material forming any suitable shapes with any suitable fill percentages having any suitable patterns.

Where appropriate, the shapes of the electrodes (or other elements) of a touch sensor may constitute in whole or in part one or more macro-features of the touch sensor. One or more characteristics of the implementation of those shapes (such as, for example, the conductive materials, fills, or patterns within the shapes) may constitute in whole or in part one or more micro-features of the touch sensor. One or more macro-features of a touch sensor may determine one or more characteristics of its functionality, and one or more micro-features of the touch sensor may determine one or more optical features of the touch sensor, such as transmittance, refraction, or reflection.

A mechanical stack may contain the substrate (or multiple substrates) and the conductive material forming the drive or sense electrodes of touch sensor 10. As an example and not by way of limitation, the mechanical stack may include a first layer of optically clear adhesive (OCA) beneath a cover panel. The cover panel may be clear and made of a resilient material suitable for repeated touching, such as for example glass, polycarbonate, or poly(methyl methacrylate) (PMMA). This disclosure contemplates any suitable cover panel made of any suitable material. The first layer of OCA may be disposed between the cover panel and the substrate with the conductive material forming the drive or sense electrodes. The mechanical stack may also include a second layer of OCA and a dielectric layer (which may be made of PET or another suitable material, similar to the substrate with the conductive material forming the drive or sense electrodes). As an alternative, where appropriate, a thin coating of a dielectric material may be applied instead of the second layer of OCA and the dielectric layer. The second layer of OCA may be disposed between the substrate with the conductive material making up the drive or sense electrodes and the dielectric layer, and the dielectric layer may be disposed between the second layer of OCA and an air gap to a display of a device including touch sensor 10 and touch-sensor controller 12. As an example only and not by way of limitation, the cover panel may have a thickness of approximately 1 mm; the first layer of OCA may have a thickness of approximately 0.05 mm; the substrate with the conductive material forming the drive or sense electrodes may have a thickness of approximately 0.05 mm; the second layer of OCA may have a thickness of approximately 0.05 mm; and the dielectric layer may have a thickness of approximately 0.05 mm. Although this disclosure describes a particular mechanical stack with a particular number of particular layers made of particular materials and having particular thicknesses, this disclosure contemplates any suitable mechanical stack with any suitable number of any suitable layers made of any suitable materials and having any suitable thicknesses. As an example and not by way of limitation, in particular embodiments, a layer of adhesive or dielectric may replace the dielectric layer, second layer of OCA, and air gap described above, with there being no air gap to the display.

One or more portions of the substrate of touch sensor 10 may be made of polyethylene terephthalate (PET) or another suitable material. This disclosure contemplates any suitable substrate with any suitable portions made of any suitable material. In particular embodiments, the drive or sense electrodes in touch sensor 10 may be made of ITO in whole or in part. In particular embodiments, the drive or sense electrodes in touch sensor 10 may be made of fine lines of metal or other conductive material. As an example and not by way of limitation, one or more portions of the conductive material may be copper or copper-based and have a thickness of approximately 5 μm or less and a width of approximately 10 μm or less. As another example, one or more portions of the conductive material may be silver or silver-based and similarly have a thickness of approximately 5 μm or less and a width of approximately 10 μm or less. This disclosure contemplates any suitable electrodes made of any suitable material.

Touch sensor 10 may implement a capacitive form of touch sensing. In a mutual-capacitance implementation, touch sensor 10 may include an array of drive and sense electrodes forming an array of capacitive nodes. A drive electrode and a sense electrode may form a capacitive node. The drive and sense electrodes forming the capacitive node may come near each other, but not make electrical contact with each other. Instead, the drive and sense electrodes may be capacitively coupled to each other across a space between them. A pulsed or alternating voltage applied to the drive electrode (by touch-sensor controller 12) may induce a charge on the sense electrode, and the amount of charge induced may be susceptible to external influence (such as a touch or the proximity of an object). When an object touches or comes within proximity of the capacitive node, a change in capacitance may occur at the capacitive node and touch-sensor controller 12 may measure the change in capacitance. By measuring changes in capacitance throughout the array, touch-sensor controller 12 may determine the position of the touch or proximity within the touch-sensitive area(s) of touch sensor 10.

In a self-capacitance implementation, touch sensor 10 may include an array of electrodes of a single type that may each form a capacitive node. When an object touches or comes within proximity of the capacitive node, a change in self-capacitance may occur at the capacitive node and touch-sensor controller 12 may measure the change in capacitance, for example, as a change in the amount of charge needed to raise the voltage at the capacitive node by a pre-determined amount. As with a mutual-capacitance implementation, by measuring changes in capacitance throughout the array, touch-sensor controller 12 may determine the position of the touch or proximity within the touch-sensitive area(s) of touch sensor 10. This disclosure contemplates any suitable form of capacitive touch sensing, where appropriate.

In particular embodiments, one or more drive electrodes may together form a drive line running horizontally or vertically or in any suitable orientation. Similarly, one or more sense electrodes may together form a sense line running horizontally or vertically or in any suitable orientation. In particular embodiments, drive lines may run substantially perpendicular to sense lines. Herein, reference to a drive line may encompass one or more drive electrodes making up the drive line, and vice versa, where appropriate. Similarly, reference to a sense line may encompass one or more sense electrodes making up the sense line, and vice versa, where appropriate.

Touch sensor 10 may have drive and sense electrodes disposed in a pattern on one side of a single substrate. In such a configuration, a pair of drive and sense electrodes capacitively coupled to each other across a space between them may form a capacitive node. For a self-capacitance implementation, electrodes of only a single type may be disposed in a pattern on a single substrate. In addition or as an alternative to having drive and sense electrodes disposed in a pattern on one side of a single substrate, touch sensor 10 may have drive electrodes disposed in a pattern on one side of a substrate and sense electrodes disposed in a pattern on another side of the substrate. Moreover, touch sensor 10 may have drive electrodes disposed in a pattern on one side of one substrate and sense electrodes disposed in a pattern on one side of another substrate. In such configurations, an intersection of a drive electrode and a sense electrode may form a capacitive node. Such an intersection may be a location where the drive electrode and the sense electrode “cross” or come nearest each other in their respective planes. The drive and sense electrodes do not make electrical contact with each other—instead they are capacitively coupled to each other across a dielectric at the intersection. Although this disclosure describes particular configurations of particular electrodes forming particular nodes, this disclosure contemplates any suitable configuration of any suitable electrodes forming any suitable nodes. Moreover, this disclosure contemplates any suitable electrodes disposed on any suitable number of any suitable substrates in any suitable patterns.

As described above, a change in capacitance at a capacitive node of touch sensor 10 may indicate a touch or proximity input at the position of the capacitive node. Touch-sensor controller 12 may detect and process the change in capacitance to determine the presence and location of the touch or proximity input. Touch-sensor controller 12 may then communicate information about the touch or proximity input to one or more other components (such one or more central processing units (CPUs)) of a device that includes touch sensor 10 and touch-sensor controller 12, which may respond to the touch or proximity input by initiating a function of the device (or an application running on the device). Although this disclosure describes a particular touch-sensor controller having particular functionality with respect to a particular device and a particular touch sensor, this disclosure contemplates any suitable touch-sensor controller having any suitable functionality with respect to any suitable device and any suitable touch sensor.

Touch-sensor controller 12 may be one or more integrated circuits (ICs), such as for example general-purpose microprocessors, microcontrollers, programmable logic devices or arrays, application-specific ICs (ASICs). In particular embodiments, touch-sensor controller 12 comprises analog circuitry, digital logic, and digital non-volatile memory. In particular embodiments, touch-sensor controller 12 is disposed on a flexible printed circuit (FPC) bonded to the substrate of touch sensor 10, as described below. The FPC may be active or passive, where appropriate. In particular embodiments, multiple touch-sensor controllers 12 are disposed on the FPC. Touch-sensor controller 12 may include a processor unit, a drive unit, a sense unit, and a storage unit. The drive unit may supply drive signals to the drive electrodes of touch sensor 10. The sense unit may sense charge at the capacitive nodes of touch sensor 10 and provide measurement signals to the processor unit representing capacitances at the capacitive nodes. The processor unit may control the supply of drive signals to the drive electrodes by the drive unit and process measurement signals from the sense unit to detect and process the presence and location of a touch or proximity input within the touch-sensitive area(s) of touch sensor 10. The processor unit may also track changes in the position of a touch or proximity input within the touch-sensitive area(s) of touch sensor 10. The storage unit may store programming for execution by the processor unit, including programming for controlling the drive unit to supply drive signals to the drive electrodes, programming for processing measurement signals from the sense unit, and other suitable programming, where appropriate. Although this disclosure describes a particular touch-sensor controller having a particular implementation with particular components, this disclosure contemplates any suitable touch-sensor controller having any suitable implementation with any suitable components.

Tracks 14 of conductive material disposed on the substrate of touch sensor 10 may couple the drive or sense electrodes of touch sensor 10 to connection pads 16, also disposed on the substrate of touch sensor 10. As described below, connection pads 16 facilitate coupling of tracks 14 to touch-sensor controller 12. Tracks 14 may extend into or around (e.g. at the edges of) the touch-sensitive area(s) of touch sensor 10. Particular tracks 14 may provide drive connections for coupling touch-sensor controller 12 to drive electrodes of touch sensor 10, through which the drive unit of touch-sensor controller 12 may supply drive signals to the drive electrodes. Other tracks 14 may provide sense connections for coupling touch-sensor controller 12 to sense electrodes of touch sensor 10, through which the sense unit of touch-sensor controller 12 may sense charge at the capacitive nodes of touch sensor 10. Tracks 14 may be made of fine lines of metal or other conductive material. As an example and not by way of limitation, the conductive material of tracks 14 may be copper or copper-based and have a width of approximately 100 μm or less. As another example, the conductive material of tracks 14 may be silver or silver-based and have a width of approximately 100 μm or less. In particular embodiments, tracks 14 may be made of ITO in whole or in part in addition or as an alternative to fine lines of metal or other conductive material. Although this disclosure describes particular tracks made of particular materials with particular widths, this disclosure contemplates any suitable tracks made of any suitable materials with any suitable widths. In addition to tracks 14, touch sensor 10 may include one or more ground lines terminating at a ground connector (which may be a connection pad 16) at an edge of the substrate of touch sensor 10 (similar to tracks 14).

Connection pads 16 may be located along one or more edges of the substrate, outside the touch-sensitive area(s) of touch sensor 10. As described above, touch-sensor controller 12 may be on an FPC. Connection pads 16 may be made of the same material as tracks 14 and may be bonded to the FPC using an anisotropic conductive film (ACF). Connection 18 may include conductive lines on the FPC coupling touch-sensor controller 12 to connection pads 16, in turn coupling touch-sensor controller 12 to tracks 14 and to the drive or sense electrodes of touch sensor 10. In another embodiment, connection pads 16 may be connected to an electro-mechanical connector (such as a zero insertion force wire-to-board connector); in this embodiment, connection 18 may not need to include an FPC. This disclosure contemplates any suitable connection 18 between touch-sensor controller 12 and touch sensor 10.

FIG. 2 illustrates example mesh cells with example vertices having substantially randomized locations. Although this disclosure describes and illustrates a particular distribution of seed locations, this disclosure contemplates any suitable distribution of seed locations. Moreover, although this disclosure describes and illustrates particular vertices defining particular mesh cells or microfeatures in particular configurations, this disclosure contemplates any suitable vertices defining any suitable mesh cells or microfeatures in any suitable configuration. Area 20 may correspond to a portion of a drive or sense electrode (or other element) of a touch sensor. In a touch sensor, mesh segments 70 connecting pairs of adjacent vertices 74 may correspond to fine lines of metal (such as for example copper, silver, or a copper- or silver-based material) or other conductive material with a thickness of approximately 1 μm or less and a width of approximately 5 μm or less. Seed locations 72, on the other hand, do not correspond to any conductive or other material in the touch sensor. Instead, they may serve as a basis to determine at least in part the arrangement of vertices 74, as described below. In particular embodiments, mesh cells 76 may be defined at least in part by two pairs of opposing vertices 74 and associated mesh segments 70. Although this disclosure describes and illustrates particular mesh cells with a particular number and configuration of vertices and mesh segments, this disclosure contemplates any suitable mesh cell with any suitable number of vertices and mesh segments.

In particular embodiments, seed locations 72 may be distributed throughout area 20 in a two-dimensional (2D) substantially regularly spaced pattern. In particular embodiments, seed locations 72 may be distributed based at least in part on vertices 74 of an initial mesh cell (e.g. 76A). As an example and not by way of limitation, seed locations 72 of the initial mesh cell (e.g. 76A) may have an initial distribution. As described below, vertices 74 of the initial mesh cell (e.g. 76A) may be determined through an annulus 78 of each vertex 74 of the initial mesh cell. Furthermore, seed locations 72 of subsequent mesh cells (e.g. 76B) may be determined based at least in part on the vertices 74 of the initial mesh cell (e.g. 76A). Although this disclosure describes and illustrates particular distribution of seed locations, this disclosure contemplates any suitable distribution of seed locations, such as for example a substantially random distribution.

Vertices 74 of mesh cells 76A-B may be arranged in a substantially randomized pattern that may reduce the occurrence of repeating patterns or frequencies among mesh segments 70, which may in turn reduce the occurrence of moiré patterns with respect to a display visible through area 20. In particular embodiments, each seed location 72 may have an associated annulus 78 substantially centered about each seed location 72 and annulus 78 may be defined by an associated a minimum 80 and maximum 82 pre-determined radii. As an example and not by way of limitation, a dimension of minimum 80 and maximum 82 pre-determined radii may be determined based at least in part of one or more dimensions of an display underneath area 20. In particular embodiments, a location of each vertex 74 may be substantially randomly distributed within the annulus 78 associated with each seed location 72. Furthermore, mesh segments 70 of conductive material may couple adjacent pairs of vertices 74 as described above.

FIG. 3 illustrates an example dual-layer mesh pattern with substantially randomized vertices. The example of FIG. 2 illustrates a single-sided implementation, but this disclosure contemplates any suitable n-sided implementation and is not limited to a singled-sided implementation. As described above, area 20 may correspond to a portion of a drive or sense electrode (or other element) of a touch sensor. In particular embodiments, a dual-layer mesh pattern over area 20 may include a second mesh of conductive material separated from a first mesh of conductive material at least by a thickness of a dielectric layer. As an example and not by way of limitation, a first conductive mesh may be formed on a first substrate and a second conductive mesh may be formed on a second substrate. As another example, the first and second conductive meshes may be formed on a surface of a substrate with a layer of dielectric material at locations where one or more mesh segments of the second conductive mesh overlap a mesh segment of the first conductive mesh. Furthermore, the first conductive mesh may correspond to at least a portion of a drive electrode and the second conductive mesh may correspond to at least a portion of a sense electrode of a touch sensor or vice versa.

In particular embodiments, seed locations 88, and therefore one or more vertices 74B, of the second conductive mesh may be distributed based at least in part on the location of mesh cells of the first conductive mesh. As an example and not by way of limitation, the distribution of seed locations 88 of the second conductive mesh may be based at least in part on a centroid of mesh cells of the first conductive mesh defined by vertices 74 as illustrated in the example of FIG. 3. As described above, each seed location 88 of the second conductive mesh may have an associated annulus 78. As an example and not by way of limitation, the radii of annuli 78 associated with seed locations 88 may be substantially equal to the pre-determined radii of the annuli, illustrated in the example of FIG. 2, of the first conductive mesh. In particular embodiments, a location of each vertex 74B of the second conductive mesh may be substantially randomly distributed within the annulus 78 associated with each seed location 88.

As described in regard to the example of FIG. 2, mesh segments 70B of conductive material may couple adjacent pairs of vertices 74B of the second conductive mesh. In particular embodiments, one or more mesh cells 86A of the second conductive mesh may be formed by coupling adjacent pairs of vertices 74B with a minimum length mesh segment 70B. In particular embodiments, one or more mesh cells 86B of the second conductive mesh may be formed by coupling adjacent pairs of vertices 74B with one or more mesh segments 70B that overlap a mid-point location 84 of a mesh segment of the first conductive mesh, thereby forming a multi-segmented coupling between adjacent pairs of vertices 74B.

FIG. 4 illustrates an example placement of example seed locations relative to an example display. A touch sensor may be overlaid on a display to implement a touch-sensitive display device, as described below. As an example and not by way of limitation, the display underneath the touch sensor may be a liquid crystal display (LCD), a light-emitting diode (LED) display, an LED backlight LCD, an electrophoretic display, a plasma display, or other suitable display. Although this disclosure describes and illustrates a particular display configuration and display type, this disclosure contemplates any suitable device display configuration and display type. An example portion of a display may include an array of pixels 22. In the example of FIG. 4, each pixel 22 may include three sub-pixels 24. In particular embodiments, each sub-pixel 24 may correspond to a particular color, such as for example red, green, or blue. Furthermore, the combined output of sub-pixels 24 may determine the color and intensity of each pixel 22. Although this disclosure describes and illustrates pixels with a particular number of sub-pixels having particular colors, this disclosure contemplates any suitable pixels with any suitable number of sub-pixels having any suitable colors.

In particular embodiments, pixels 22 or sub-pixels 24 may be arranged in a repeating pattern along a horizontal axis 28 and a vertical axis 32 that are perpendicular to each other. Although this disclosure describes and illustrates horizontal and vertical axes, this disclosure contemplates any suitable axes having any suitable orientation. Each pixel 22 has a horizontal-pixel pitch (HPP) 26, which in particular embodiments may be defined as the distance between corresponding features of two adjacent pixels 22 along horizontal axis 28 (such as the horizontal distance from the left edge of two horizontally adjacent sub-pixels 24). Each pixel 22 has a vertical-pixel pitch (VPP) 30, which in particular embodiments may be defined as the distance between corresponding features of two adjacent pixels 22 along vertical axis 32 (such as the vertical distance from the lower edge of two vertically adjacent sub-pixels 24). This disclosure contemplates any suitable pixels with any suitable HPPs and VPPs having any suitable values.

Each pixel 22 may also include a dead space, which corresponds to regions of pixel 22 not occupied by a sub-pixel 24. In particular embodiments, the dead space has a height 34 that may be defined as the distance between adjacent sub-pixels 24 along vertical axis 32 (such as the distance between two vertically adjacent sub-pixels 24). In particular embodiments, the dead space has a width 36 that may be defined as the distance between adjacent sub-pixels 24 along horizontal axis 28 (such as the distance between two horizontally adjacent sub-pixels 24). This disclosure contemplates any suitable pixels with any suitable dead space having any suitable dimensions. Each sub-pixel 24 has a horizontal sub-pixel pitch (HSPP) 38, which may be defined in particular embodiments as the distance between corresponding features of two adjacent sub-pixels along horizontal axis 28, including width 36 of the dead space (such as the distance between the left edges of two horizontally adjacent sub-pixels 24). Each sub-pixel 24 also has a vertical sub-pixel pitch (VSPP) 40, which may be defined in particular embodiments as the distance between corresponding features of two adjacent sub-pixels along vertical axis 32, including height 34 of the dead space (such as the distance between the lower edges of two vertically adjacent sub-pixels 24).

Each sub-pixel 24 has a sub-pixel width (SPW) 42, which may be defined in particular embodiments as the dimension of a sub-pixel along horizontal axis 28 (such as the distance between the left and right edges of sub-pixel 24). Each sub-pixel 24 also has a sub-pixel height (SPH) 44, which is defined in particular embodiments as the dimension of a sub-pixel along vertical axis 32 (such as the distance between the lower and upper edges of sub-pixel 24). This disclosure contemplates any suitable sub-pixels with any suitable HSPPs, VSPPs, SPWs, and SPHs having any suitable values. In particular embodiments, pixel 22 and sub-pixel 24 may have a substantially rectangular shape, as illustrated in the example of FIG. 4. Pixel 22 and sub-pixel 24 may have other suitable shape, such as for example square, round, oval, or chevron-shaped. In the example of FIG. 4, vertical-sub-pixel pitch 40 is equal to VPP 30, and VPP 30 is equal to the sum of SPH 44 and dead-space height 34. Further, HPP 26 is equal to three times HSPP 38, and HSPP 38 is equal to the sum of sub-pixel width 42 and dead-space width 36. Although this disclosure describes and illustrates example pixels 22 and example sub-pixels 24 having particular shapes, arrangements, and dimensions, this disclosure contemplates any suitable arrangement of any suitable pixels and sub-pixels having any suitable shapes and dimensions.

In particular embodiments, seed locations (e.g. 72A-C) may be determined based at least in part on one or more dimensions of a display underneath the touch sensor. In the example of FIG. 4, a portion of seed locations (e.g. 72A-B) may be linearly disposed along a terminal side of an angle 54 relative to horizontal axis 28, and another portion of seed locations (e.g. 72B-C) may be linearly disposed along a terminal side 52 of an angle 56 relative to horizontal axis 28. In particular embodiments, the terminal side 50 of angle 54 may pass through points 58 and 60. The slope of terminal side 50 of angle 54 may be defined as the vertical rise of terminal side 50 divided by the horizontal run of terminal side 50, and angle 54 can be found from the arc tangent of the slope. In the example of FIG. 4, the vertical rise of terminal side 50 is SPH 44, and the horizontal run of terminal side 50 is HPP 26. Thus, the slope of terminal side 50 equals SPH/HPP, and angle 54 (Θ₁) can be found from the expression Θ₁=arc tan(SPH/HPP).

In the example of FIG. 4, terminal side 52 of angle 56 associated with a portion of seed locations (e.g. 72C-B) may pass through points 62 and 64. The slope of terminal side 52 of angle 56 may be defined as the vertical rise of terminal side 52 divided by the horizontal run of terminal side 52, and angle 56 can be found from the arc tangent of the slope. In the example of FIG. 4, the vertical rise of terminal side 52 is VPP 30, and the horizontal run of terminal side 52 is two times HSPP 38. Thus, the slope of terminal side 52 equals VPP/2·HSPP, and angle 56 (Θ₂) can be found from the expression Θ₂=arc tan(VPP/2·HSPP). In particular embodiments, angles Θ₁ and Θ₂ may vary by up to approximately 1° from the values calculated in the expressions above without substantially degrading the optical properties associated with the mesh pattern. Terminal sides 50 and 52, and points 58, 60, 62, and 64 do not correspond to any conductive or other material in the touch sensor and are provided for didactic purposes. Furthermore, terminal side 50 of angle 54 need not be constrained to pass through particular points 58 and 60 or seed locations 72A-B illustrated in the example of FIG. 4, but may be displaced along horizontal axis 28 and vertical axis 32 by any suitable amount. Similarly, in particular embodiments, terminal side 52 of angle 56 need not be constrained to pass through points 62 and 64 or seed locations 72B-C as illustrated in the example of FIG. 4, but may be displaced along horizontal axis 28 and vertical axis 32 by any suitable amount.

As an example and not by way of limitation, a horizontal distance 90 separating terminal side 50 of angle 54 passing through seed locations 72A and 72B, from terminal side 50 of angle 54 passing through seed locations 72C and 72D may be substantially equal to three times HPP 26 (or nine times HSPP 38). A horizontal distance 92 separating terminal side 52 of angle 56 passing through seed locations 72B and 72C, from terminal side 52 of angle 56 passing through seed locations 72A and 72E may be substantially equal to 13/6 times HPP 26 (or 6.5 times HSPP 38). Furthermore, horizontal distances 90 and 92 described above may be compatible with a display with an HPP of approximately 150 μm. As another example, horizontal distance 90 separating terminal side 50 of angle 54 passing through seed locations 72A and 72B, from terminal side 50 of angle 54 passing through seed locations 72C and 72D may be substantially equal to six times HPP 26 (or 18 times HSPP 38). Horizontal distance 92 separating terminal side 52 of angle 56 passing through seed locations 72B and 72C, from terminal side 52 of angle 56 passing through seed locations 72A and 72E may be substantially equal to 13/3 times HPP 26 (or 13 times HSPP 38). Furthermore, horizontal distances 90 and 92 described above may be compatible for a display with an HPP that is substantially less than 150 μm. As another example, horizontal distance 90 separating terminal side 50 of angle 54 passing through seed locations 72A and 72B, from terminal side 50 of angle 54 passing through seed locations 72C and 72D may be substantially equal substantially equal to two times HPP 26 (or six times HSPP 38). Horizontal distance 92 separating terminal side 52 of angle 56 passing through seed locations 72B and 72C, from terminal side 52 of angle 56 passing through seed locations 72A and 72E may be substantially equal to the sum of HPP 26, HSPP 38, dead space width 36, and ½ of sub-pixel width 42. Horizontal distances 90 and 92 described above may be compatible with a display with an HPP 26 of approximately 250 μm. Although this disclosure describes and illustrates particular horizontal distances between particular seed locations, this disclosure contemplates any suitable separation distances between any suitable seed locations.

FIG. 5 illustrates an example method for designing a conductive mesh with randomized vertices. The method may start at step 100, where a computing device may determine a number of seed locations. In particular embodiments, the seed locations may be a regularly spaced 2D pattern that may be determined at least in part on one or more dimensions of a display. At step 102, the computing device may generate a pattern for a mesh of conductive material of a touch sensor at least in part by determining a number of vertices of a number of mesh cells of the mesh of conductive material, at which point the method may end. In particular embodiments, each of the vertices may have a substantially randomized location within an annulus centered at one of the seed locations. Although this disclosure describes and illustrates particular steps of the method of FIG. 5 as occurring in a particular order, this disclosure contemplates any suitable steps of the method of FIG. 5 occurring in any suitable order. Particular embodiments may repeat one or more steps of the method of FIG. 4, where appropriate. Moreover, although this disclosure describes and illustrates an example method for designing a conductive mesh with randomized vertices including the particular steps of the method of FIG. 5, this disclosure contemplates any suitable method for designing a conductive mesh with randomized vertices including any suitable steps, which may include all, some, or none of the steps of the method of FIG. 5, where appropriate. Moreover, although this disclosure describes and illustrates particular components carrying out particular steps of the method of FIG. 5, this disclosure contemplates any suitable combination of any suitable components carrying out any suitable steps of the method of FIG. 5.

FIG. 6 illustrates an example computer system 200. In particular embodiments, one or more computer systems 200 perform one or more steps of one or more methods described or illustrated herein. In particular embodiments, one or more computer systems 200 provide functionality described or illustrated herein. In particular embodiments, software running on one or more computer systems 200 performs one or more steps of one or more methods described or illustrated herein or provides functionality described or illustrated herein. Particular embodiments include one or more portions of one or more computer systems 200. Herein, reference to a computer system may encompass a computing device, and vice versa, where appropriate. Moreover, reference to a computer system may encompass one or more computer systems, where appropriate.

This disclosure contemplates any suitable number of computer systems 200. This disclosure contemplates computer system 200 taking any suitable physical form. As example and not by way of limitation, computer system 200 may be an embedded computer system, a system-on-chip (SOC), a single-board computer system (SBC) (such as, for example, a computer-on-module (COM) or system-on-module (SOM)), a desktop computer system, a laptop or notebook computer system, an interactive kiosk, a mainframe, a mesh of computer systems, a mobile telephone, a personal digital assistant (PDA), a server, a tablet computer system, or a combination of two or more of these. Where appropriate, computer system 200 may include one or more computer systems 200; be unitary or distributed; span multiple locations; span multiple machines; span multiple data centers; or reside in a cloud, which may include one or more cloud components in one or more networks. Where appropriate, one or more computer systems 200 may perform without substantial spatial or temporal limitation one or more steps of one or more methods described or illustrated herein. As an example and not by way of limitation, one or more computer systems 200 may perform in real time or in batch mode one or more steps of one or more methods described or illustrated herein. One or more computer systems 200 may perform at different times or at different locations one or more steps of one or more methods described or illustrated herein, where appropriate.

In particular embodiments, computer system 200 includes a processor 202, memory 204, storage 206, an input/output (I/O) interface 208, a communication interface 210, and a bus 212. Although this disclosure describes and illustrates a particular computer system having a particular number of particular components in a particular arrangement, this disclosure contemplates any suitable computer system having any suitable number of any suitable components in any suitable arrangement.

In particular embodiments, processor 202 includes hardware for executing instructions, such as those making up a computer program. As an example and not by way of limitation, to execute instructions, processor 202 may retrieve (or fetch) the instructions from an internal register, an internal cache, memory 204, or storage 206; decode and execute them; and then write one or more results to an internal register, an internal cache, memory 204, or storage 206. In particular embodiments, processor 202 may include one or more internal caches for data, instructions, or addresses. This disclosure contemplates processor 202 including any suitable number of any suitable internal caches, where appropriate. As an example and not by way of limitation, processor 202 may include one or more instruction caches, one or more data caches, and one or more translation lookaside buffers (TLBs). Instructions in the instruction caches may be copies of instructions in memory 204 or storage 206, and the instruction caches may speed up retrieval of those instructions by processor 202. Data in the data caches may be copies of data in memory 204 or storage 206 for instructions executing at processor 202 to operate on; the results of previous instructions executed at processor 202 for access by subsequent instructions executing at processor 202 or for writing to memory 204 or storage 206; or other suitable data. The data caches may speed up read or write operations by processor 202. The TLBs may speed up virtual-address translation for processor 202. In particular embodiments, processor 202 may include one or more internal registers for data, instructions, or addresses. This disclosure contemplates processor 202 including any suitable number of any suitable internal registers, where appropriate. Where appropriate, processor 202 may include one or more arithmetic logic units (ALUs); be a multi-core processor; or include one or more processors 202. Although this disclosure describes and illustrates a particular processor, this disclosure contemplates any suitable processor.

In particular embodiments, memory 204 includes main memory for storing instructions for processor 202 to execute or data for processor 202 to operate on. As an example and not by way of limitation, computer system 200 may load instructions from storage 206 or another source (such as, for example, another computer system 200) to memory 204. Processor 202 may then load the instructions from memory 204 to an internal register or internal cache. To execute the instructions, processor 202 may retrieve the instructions from the internal register or internal cache and decode them. During or after execution of the instructions, processor 202 may write one or more results (which may be intermediate or final results) to the internal register or internal cache. Processor 202 may then write one or more of those results to memory 204. In particular embodiments, processor 202 executes only instructions in one or more internal registers or internal caches or in memory 204 (as opposed to storage 206 or elsewhere) and operates only on data in one or more internal registers or internal caches or in memory 204 (as opposed to storage 206 or elsewhere). One or more memory buses (which may each include an address bus and a data bus) may couple processor 202 to memory 204. Bus 212 may include one or more memory buses, as described below. In particular embodiments, one or more memory management units (MMUs) reside between processor 202 and memory 204 and facilitate accesses to memory 204 requested by processor 202. In particular embodiments, memory 204 includes random access memory (RAM). This RAM may be volatile memory, where appropriate Where appropriate, this RAM may be dynamic RAM (DRAM) or static RAM (SRAM). Moreover, where appropriate, this RAM may be single-ported or multi-ported RAM. This disclosure contemplates any suitable RAM. Memory 204 may include one or more memories 204, where appropriate. Although this disclosure describes and illustrates particular memory, this disclosure contemplates any suitable memory.

In particular embodiments, storage 206 includes mass storage for data or instructions. As an example and not by way of limitation, storage 206 may include a hard disk drive (HDD), a floppy disk drive, flash memory, an optical disc, a magneto-optical disc, magnetic tape, or a Universal Serial Bus (USB) drive or a combination of two or more of these. Storage 206 may include removable or non-removable (or fixed) media, where appropriate. Storage 206 may be internal or external to computer system 200, where appropriate. In particular embodiments, storage 206 is non-volatile, solid-state memory. In particular embodiments, storage 206 includes read-only memory (ROM). Where appropriate, this ROM may be mask-programmed ROM, programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), electrically alterable ROM (EAROM), or flash memory or a combination of two or more of these. This disclosure contemplates mass storage 206 taking any suitable physical form. Storage 206 may include one or more storage control units facilitating communication between processor 202 and storage 206, where appropriate. Where appropriate, storage 206 may include one or more storages 206. Although this disclosure describes and illustrates particular storage, this disclosure contemplates any suitable storage.

In particular embodiments, I/O interface 208 includes hardware, software, or both, providing one or more interfaces for communication between computer system 200 and one or more I/O devices. Computer system 200 may include one or more of these I/O devices, where appropriate. One or more of these I/O devices may enable communication between a person and computer system 200. As an example and not by way of limitation, an I/O device may include a keyboard, keypad, microphone, monitor, mouse, printer, scanner, speaker, still camera, stylus, tablet, touch screen, trackball, video camera, another suitable I/O device or a combination of two or more of these. An I/O device may include one or more sensors. This disclosure contemplates any suitable I/O devices and any suitable I/O interfaces 208 for them. Where appropriate, I/O interface 208 may include one or more device or software drivers enabling processor 202 to drive one or more of these I/O devices. I/O interface 208 may include one or more I/O interfaces 208, where appropriate. Although this disclosure describes and illustrates a particular I/O interface, this disclosure contemplates any suitable I/O interface.

In particular embodiments, communication interface 210 includes hardware, software, or both providing one or more interfaces for communication (such as, for example, packet-based communication) between computer system 200 and one or more other computer systems 200 or one or more networks. As an example and not by way of limitation, communication interface 210 may include a network interface controller (NIC) or network adapter for communicating with an Ethernet or other wire-based network or a wireless NIC (WNIC) or wireless adapter for communicating with a wireless network, such as a WI-FI network. This disclosure contemplates any suitable network and any suitable communication interface 210 for it. As an example and not by way of limitation, computer system 200 may communicate with an ad hoc network, a personal area network (PAN), a local area network (LAN), a wide area network (WAN), a metropolitan area network (MAN), or one or more portions of the Internet or a combination of two or more of these. One or more portions of one or more of these networks may be wired or wireless. As an example, computer system 200 may communicate with a wireless PAN (WPAN) (such as, for example, a BLUETOOTH WPAN), a WI-FI network, a WI-MAX network, a cellular telephone network (such as, for example, a Global System for Mobile Communications (GSM) network), or other suitable wireless network or a combination of two or more of these. Computer system 200 may include any suitable communication interface 210 for any of these networks, where appropriate. Communication interface 210 may include one or more communication interfaces 210, where appropriate. Although this disclosure describes and illustrates a particular communication interface, this disclosure contemplates any suitable communication interface.

In particular embodiments, bus 212 includes hardware, software, or both coupling components of computer system 200 to each other. As an example and not by way of limitation, bus 212 may include an Accelerated Graphics Port (AGP) or other graphics bus, an Enhanced Industry Standard Architecture (EISA) bus, a front-side bus (FSB), a HYPERTRANSPORT (HT) interconnect, an Industry Standard Architecture (ISA) bus, an INFINIBAND interconnect, a low-pin-count (LPC) bus, a memory bus, a Micro Channel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCIe) bus, a serial advanced technology attachment (SATA) bus, a Video Electronics Standards Association local (VLB) bus, or another suitable bus or a combination of two or more of these. Bus 212 may include one or more buses 212, where appropriate. Although this disclosure describes and illustrates a particular bus, this disclosure contemplates any suitable bus or interconnect.

Herein, a computer-readable non-transitory storage medium or media may include one or more semiconductor-based or other integrated circuits (ICs) (such, as for example, field-programmable gate arrays (FPGAs) or application-specific ICs (ASICs)), hard disk drives (HDDs), hybrid hard drives (HHDs), optical discs, optical disc drives (ODDs), magneto-optical discs, magneto-optical drives, floppy diskettes, floppy disk drives (FDDs), magnetic tapes, solid-state drives (SSDs), RAM-drives, SECURE DIGITAL cards or drives, any other suitable computer-readable non-transitory storage media, or any suitable combination of two or more of these, where appropriate. A computer-readable non-transitory storage medium may be volatile, non-volatile, or a combination of volatile and non-volatile, where appropriate.

Herein, “or” is inclusive and not exclusive, unless expressly indicated otherwise or indicated otherwise by context. Therefore, herein, “A or B” means “A, B, or both,” unless expressly indicated otherwise or indicated otherwise by context. Moreover, “and” is both joint and several, unless expressly indicated otherwise or indicated otherwise by context. Therefore, herein, “A and B” means “A and B, jointly or severally,” unless expressly indicated otherwise or indicated otherwise by context.

The scope of this disclosure encompasses all changes, substitutions, variations, alterations, and modifications to the example embodiments described or illustrated herein that a person having ordinary skill in the art would comprehend. The scope of this disclosure is not limited to the example embodiments described or illustrated herein. Moreover, although this disclosure describes and illustrates respective embodiments herein as including particular components, elements, feature, functions, operations, or steps, any of these embodiments may include any combination or permutation of any of the components, elements, features, functions, operations, or steps described or illustrated anywhere herein that a person having ordinary skill in the art would comprehend. Furthermore, reference in the appended claims to an apparatus or system or a component of an apparatus or system being adapted to, arranged to, capable of, configured to, enabled to, operable to, or operative to perform a particular function encompasses that apparatus, system, component, whether or not it or that particular function is activated, turned on, or unlocked, as long as that apparatus, system, or component is so adapted, arranged, capable, configured, enabled, operable, or operative. 

What is claimed is:
 1. One or more non-transitory computer-readable storage media embodying logic that is configured to, when executed by one or more processors, cause the one or more processors to perform operations comprising: determining a plurality of seed locations of a conductive mesh; determining a plurality of annuli that are substantially centered about a respective seed location of the plurality of seed locations, wherein the plurality of annuli are defined by a first and second radius from the respective seed location of the annulus; determining a location for a plurality of vertices, the plurality of vertices having a substantially randomized location within a respective annulus of the plurality of annuli; and defining a mesh segment of conductive material connecting a pair of adjacent vertices.
 2. The one or more non-transitory computer-readable storage media of claim 1, wherein one or more of the seed locations are determined relative to a display, the display comprising a plurality of pixels that each comprise sub-pixels, each of the pixels having a first pixel pitch along a first axis and a second pixel pitch along a second axis that is perpendicular to the first axis, each of the sub-pixels having a first sub-pixel pitch along the first axis, a first sub-pixel dimension along the first axis, and a second sub-pixel dimension along the second axis.
 3. The one or more non-transitory computer-readable storage media of claim 2, wherein the vertices of each mesh cell comprise: a terminal side of a first angle relative to the first axis comprising a first seed location and a second seed location, the first angle being at least approximately equal to an arc tangent of the ratio of the second sub-pixel dimension to the first pixel pitch; and a terminal side of a second angle relative to the first axis comprising the second seed location and a third seed location, the second angle being at least approximately equal to an arc tangent of the ratio of the second pixel pitch to twice the first sub-pixel pitch, wherein the first and third seed locations being opposing seed locations of the mesh cell, the second seed location being adjacent to the first and third seed locations.
 4. The one or more non-transitory computer-readable storage media of claim 3, wherein a distance separating the first seed location from the second seed location is at least approximately equal to three times the first pixel pitch and a distance separating the second seed location from the third seed location is at least approximately equal to 13/6 of the first pixel pitch.
 5. The one or more non-transitory computer-readable storage media of claim 3, wherein a distance separating the first seed location from the second seed location is at least approximately equal to six times the first pixel pitch; and a distance separating the second seed location from the third seed location is at least approximately equal to 13/3 of the first pixel pitch.
 6. The one or more non-transitory computer-readable storage media of claim 3, wherein each of the sub-pixels has a first sub-pixel dead space dimension along the first axis, a distance separating the first seed location from the second seed location is at least approximately equal to two times the first pixel pitch, a distance separating the second seed location from the third seed location is at least approximately equal to a sum of: the first pixel pitch; the first sub-pixel pitch; and the first sub-pixel dead space dimension; and a half of the first sub-pixel dimension.
 7. The one or more non-transitory computer-readable storage media of claim 1, wherein the conductive mesh further comprises an initial mesh cell with four seed locations and seed locations of a subsequent mesh cell are determined based at least in part on the vertices of the initial mesh cell.
 8. The one or more non-transitory computer-readable storage media of claim 1, wherein: the conductive mesh further comprises a first subset of mesh cells separated from a second subset of mesh cells by at least a thickness of a dielectric layer; and the seed location of each vertex of the second subset of mesh cells is within a centroid of each mesh cell of the first subset of mesh cells.
 9. The one or more non-transitory computer-readable storage media of claim 8, wherein one or more of the mesh segments coupling adjacent vertices of the second subset of mesh cells overlap a midpoint of a mesh segment coupling adjacent vertices of the first subset of mesh cells.
 10. A touch sensor comprising: an electrode comprising a mesh of conductive material, the mesh of conductive material comprising a plurality of mesh cells, a particular mesh cell of the mesh cells comprising: a plurality of vertices having substantially randomized locations, respectively, within an annulus centered at a respective seed location, wherein a distance separates a vertex positioned within the respective annulus for the vertex from the respective seed location for the vertex, wherein the annulus is defined by a first and second radius from the respective seed location; and a mesh segment of conductive material that connects a pair of adjacent vertices.
 11. The touch sensor of claim 10, wherein one or more of the seed locations are determined relative to a display, the display comprising a plurality of pixels that each comprise sub-pixels, each of the pixels having a first pixel pitch along a first axis and a second pixel pitch along a second axis that is perpendicular to the first axis, each of the sub-pixels having a first sub-pixel pitch along the first axis, a first sub-pixel dimension along the first axis, and a second sub-pixel dimension along the second axis.
 12. The touch sensor of claim 11, wherein the vertices of the particular mesh cell comprise: a terminal side of a first angle relative to the first axis comprising a first seed location and a second seed location, the first angle being at least approximately equal to an arc tangent of the ratio of the second sub-pixel dimension to the first pixel pitch; and a terminal side of a second angle relative to the first axis comprising the second seed location and a third seed location, the second angle being at least approximately equal to an arc tangent of the ratio of the second pixel pitch to twice the first sub-pixel pitch, wherein the first and third seed locations being opposing seed locations of the mesh cell, the second seed location being adjacent to the first and third seed locations.
 13. A method comprising: by a computing device, determining a plurality of seed locations of a conductive mesh; by the computing device, determining a plurality of annuli that are substantially centered about a respective seed location of the plurality of seed locations, wherein the plurality of annuli are defined by a first and second radius from the respective seed location of the annulus; by the computing device, determining a location for a plurality of vertices the plurality of vertices having a substantially randomized location within a respective annulus of the plurality of annuli; and connecting a pair of adjacent vertices with a mesh segment of conductive material, wherein the mesh segments define a mesh cell.
 14. The method of claim 13, wherein: one or more of the seed locations are determined relative to a display, the display comprising a plurality of pixels that each comprise sub-pixels, each of the pixels having a first pixel pitch along a first axis and a second pixel pitch along a second axis that is perpendicular to the first axis, each of the sub-pixels having a first sub-pixel pitch along the first axis, a first sub-pixel dimension along the first axis, and a second sub-pixel dimension along the second axis; the vertices of each mesh cell comprise a terminal side of a first angle relative to the first axis comprising a first seed location and a second seed location, the first angle being at least approximately equal to an arc tangent of the ratio of the second sub-pixel dimension to the first pixel pitch, a terminal side of a second angle relative to the first axis comprising the second seed location and a third seed location, the second angle being at least approximately equal to an arctangent of the ratio of the second pixel pitch to twice the first sub-pixel pitch; and the first and third seed locations are opposing seed locations of the mesh cell, the second seed location being adjacent to the first and third seed locations.
 15. The method of claim 14, wherein a distance separating the first seed location from the second seed location is at least approximately equal to three times the first pixel pitch and a distance separating the second seed location from the third seed location is at least approximately equal to 13/6 of the first pixel pitch.
 16. The method of claim 14, wherein a distance separating the first seed location from the second seed location is at least approximately equal to six times the first pixel pitch; and a distance separating the second seed location from the third seed location is at least approximately equal to 13/3 of the first pixel pitch.
 17. The method of claim 14, wherein each of the sub-pixels has a first sub-pixel dead space dimension along the first axis, a distance separating the first seed location from the second seed location is at least approximately equal to two times the first pixel pitch, a distance separating the second seed location from the third seed location is at least approximately equal to a sum of: the first pixel pitch; the first sub-pixel pitch; and the first sub-pixel dead space dimension; and a half of the first sub-pixel dimension.
 18. The method of claim 13, wherein the mesh further comprises an initial mesh cell with four seed locations and seed locations of a subsequent mesh cell are determined based at least in part on the vertices of the initial mesh cell.
 19. The method of claim 13, wherein: the mesh further comprises a first subset of mesh cells separated from a second subset of mesh cells by at least a thickness of a dielectric layer; and the seed location of each vertex of the second subset of mesh cells is within a centroid of each mesh cell of the first subset of mesh cells.
 20. The method of claim 19, wherein one or more mesh segments coupling adjacent vertices of the second subset of mesh cells overlap a midpoint of a mesh segment coupling adjacent vertices of the first subset of mesh cells.
 21. A conductive mesh, prepared by a process comprising: determining a plurality of seed locations; determining a plurality of annuli that are substantially centered about a respective seed location of the plurality of seed locations, wherein the plurality of annuli are defined by a first and second radius from the respective seed location of the annulus; determining a location for a plurality of vertices, the plurality of vertices having a substantially randomized location within a respective annulus of the plurality of annuli; and connecting a pair of adjacent vertices with a mesh segment of conductive material, wherein the mesh segments define a mesh cell. 